Chris, Ken and Dan have all done these, as well as folks on the forum I haven't met yet, so you will probably get a bunch of different ways!
If Grant gets on here again, he built his Spikey to be bullet proof and last forever (or at least until the Sun kills the fabric).
You might want to ask how he did it.

This is probably how it was recommended in the plans that are floating around, but this is how I recall doing it.

I hot cut the circle out of the pentagon first, then I drew a sewing line around an inch outside of the circle.
I sewed up the side of the cone to make it, well, a cone.
Then I folded under some of the bottom of the cone and matched it to the circle. Adjusting the size of the folded under bit so that the cone matched my circle more or less. Then I started sewing down the cone. It was probably about as awkward as it sounds.
You could probably make it more to your style by using some double sided tape to hold down the cone before you sew.

I used a straight stitch, and my cones are still attached despite kids standing on either side of Mimi and playing tug-of-war by pulling on the cones.

Babbman about the only thing different that I did was hot tacked the edge of the cone ALL the way around, before sewing it to the ball. That way I was able to make sure it stayed in place while sewing it on. If you dont tape/tack it in place it may end up walking off the route of the circle. Straight stitch here too. That way it is easier to control then a zig zag stich. It also looks neater too, zig and circles look messy IMHO.

Now lets see who else will chime in and then your head will start spinning and explode.